Interaction-Flip Identities in Spin Glasses
Mathematical Physics
2009-11-13 v2 Disordered Systems and Neural Networks
math.MP
Abstract
We study the properties of fluctuation for the free energies and internal energies of two spin glass systems that differ for having some set of interactions flipped. We show that their difference has a variance that grows like the volume of the flipped region. Using a new interpolation method, which extends to the entire circle the standard interpolation technique, we show by integration by parts that the bound imply new overlap identities for the equilibrium state. As a side result the case of the non-interacting random field is analyzed and the triviality of its overlap distribution proved.
Keywords
Cite
@article{arxiv.0811.2472,
title = {Interaction-Flip Identities in Spin Glasses},
author = {Pierluigi Contucci and Cristian Giardina and Claudio Giberti},
journal= {arXiv preprint arXiv:0811.2472},
year = {2009}
}
Comments
To appear on the Brezin-Parisi special issue of Journal of Statistical Physics